Abstract
In this paper, the researcher introduces the general iterative scheme for finding a common element of the set of equilibrium problems and fixed point problems of a countable family of nonexpansive mappings in Hilbert spaces. The results presented in this paper improve and extend the corresponding results announced by many others. MSC: 47H10; 47H09
Highlights
Let H be a real Hilbert space with the inner product ·, · and the norm ·
Let F be a bifunction from C × C into R, where R is the set of real numbers
Optimization and economics reduce to finding a solution of ( . ). ( ) The mappings {Tn}n∈N are said to be a family of nonexpansive mappings from H into itself if
Summary
Let H be a real Hilbert space with the inner product ·, · and the norm ·. Marino and Xu [ ] introduced the following general iterative method: xn+ = (I – αnA)Txn + αnγ f (xn), n ≥ , where A is a strongly positive bounded linear operator on H. They proved that if the sequence {αn} of parameters satisfies appropriate conditions, the sequence {xn} generated by ) converges strongly to the unique solution of the variational inequality (A – γ f )x∗, x – x∗ ≥ , x ∈ C, which is the optimality condition for the minimization problem min Ax, x – h(x), x∈C where h is a potential function for γ f (i.e., h (x) = γ f (x) for x ∈ H). {Tn}∞ n= be a sequence of nonexpansive mappings from C to C such that the common fixed point set (Tn)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
